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Variational analysis of energy-enstrophy theories on the sphere

Pages: 611 - 620, Issue Special, August 2005

 Abstract        Full Text (211.5K)              

Chjan C. Lim - Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, United States (email)
Da Zhu - Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, United States (email)

Abstract: Kraichnan's energy-enstrophy theory for 2D inviscid flows on the sphere is discussed within a variational framework. We will give necessary and sufficient conditions for the existence and uniqueness for the extremals of the energy with zero circulation under different values of the temperature parameter $\beta$. The unboundedness of the augmented energy functional in this model when $\beta$ is located in the certain intervals will be shown and related to energy catastrophe of the energy-enstrophy model.

Keywords:  variational analysis, energy-enstrophy, unboundedness.
Mathematics Subject Classification:  Primary: 76B47, 82B20; Secondary: 65C05.

Received: September 2004;      Revised: April 2005;      Published: September 2005.